A lilac bathroom would be gorgeous! I'd paint the brown wood cabinet and mirror frame white. And the door in the kitchen something other than the wall colour. The house will sigh with relief once you're done. What were they thinking!?

I know the colors aren't to your taste but you could play with them a little. In the bath you could sponge a lavender glaze over the bright pink and it could make it much more interesting. In the kitchen you could mask either vertical stripes or some sort of leaf ot branch pattern and paint another color over what is there. It could give a unique look. I will admit that I have a tendency to paint things over completely but if the budget is tight glazes seem to go a long way.

ooh my aunt has a purple bathroom and my daughter a purple bedroom. The only thing I caution you with that colour is that it fades & yelllows slightly so after maybe a year if you pick a very pale lavendar it'll look a bit greyish. I am not sure why that is. My gramma even warned me that would happen but I did it anyway.The sunny yellow kitchen sounds lovely. I did mine in a butter yellow (think subdued sunshine) and the only thing I have to say about it, is that in the twilight it looks a bit ... fluorescing. And when the lights are on it makes everything all bright and warm and glowy, especially the rich reddish brown wood, but I think it would go well with any wood coloured cabinets/tables ... natural wood is so forgiving and inviting. I love my yellow kitchen.

The color of your bathroom looks exactly like the color I painted my bedroom! But, I understand, it's not for everyone, and the former decorator really didn't take into account the colors of the wood, counter, tile, and tub surround. The lavendar room you linked to works because everything else is black and white. If everything else in the pink room was black and white, you might like it, too.

If you don't want to paint the sink base, I'd probably stay away from a cool pastel like lavendar, and go with a warmer color. What about something in the coral or peach range? Or a warm tan.